If m be the slope of a tangent to the curve e2y=1+4x2 t
![If m be the slope of a tangent to the curve e2y=1+4x2 t](/img/relate-questions.png)
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If m be the slope of a tangent to the curve e2y=1+4x2, then
A.
m < 1
B.
|M|≤1
C. |M|>1
D.
m = 2
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
We have,
e2y=1+4x2⇒e2y.2dydx=8x⇒dydx=4xe2y=4x1+4x2∴ Slope of tangent=m=4x1+4x2⇒|m|=4|x|1+4|x|2≤1⎡⎢⎣∵(1−2)|x2|≥0⇒1+4|x|2−4|x|≥0⇒4|x|1+4|x|2
Hence (b) is the correct answer.